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These sample problems below for Nonlinear Functions were generated by the MathScore.com engine.

## Sample Problems For Nonlinear Functions

Give the equation of this quadratic function. It should be in the form of 'y = ax^2' where a is an integer.
 1 2

### Complexity=3, Mode=cubic

Give the equation of this cubic function. It should be in the form of 'y = ax^3' where a is an integer.
 1 2

### Complexity=5, Mode=mixed

Give the equation of the following functions. They may be quadratic or cubic functions. They should be of the form 'y = ax^2 + b' or 'y = ax^3 + b' where a and b are integers.
 1 2

Give the equation of this quadratic function. It should be in the form of 'y = ax^2' where a is an integer.
1
Solution
The parabola opens upward so we know n > 0.
(2, 20) is in the parabola.
y = nx2
20 = n * 22
20 = 4n
n = 5
y = 5x2
2
Solution
The parabola opens upward so we know n > 0.
(2, 8) is in the parabola.
y = nx2
8 = n * 22
8 = 4n
n = 2
y = 2x2

### Complexity=3, Mode=cubic

Give the equation of this cubic function. It should be in the form of 'y = ax^3' where a is an integer.
1
Solution
The cubic function decreases as x increases so we know n < 0.
(2, -8) is in the cubic function.
y = nx3
-8 = n * 23
-8 = 8n
n = -1
y = -x3
2
Solution
The cubic function increases as x increases so we know n > 0.
(2, 24) is in the cubic function.
y = nx3
24 = n * 23
24 = 8n
n = 3
y = 3x3

### Complexity=5, Mode=mixed

Give the equation of the following functions. They may be quadratic or cubic functions. They should be of the form 'y = ax^2 + b' or 'y = ax^3 + b' where a and b are integers.
1
Solution
The function increases as x increases and doesn't open in a direction like a parabola, so it is a cubic function of the form y = nx3 + b with n > 0.
The equation intersects the y-axis at(0, 0), so
y = nx3 + b
0 = n * 03 + b
0 = b
y = nx3 0
We also know (1, 4) is in the parabola.
4 = n * 13 0
4 = n 0
n = 4
y = 4x3 0
2
Solution
The function decreases as x increases and doesn't open in a direction like a parabola, so it is a cubic function of the form y = nx3 + b with n < 0.
The equation intersects the y-axis at(0, -4), so
y = nx3 + b
-4 = n * 03 + b
-4 = b
y = nx3 -4
We also know (1, -8) is in the parabola.
-8 = n * 13 -4
-8 = n -4
n = -4
y = -4x3 -4

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